Make gap even thickness?
Try this way:

Select both sides, W - Bridge Edge Loops. Enable Merge, set Factor to 0 (or 1);
Keep current selection, V to rip, then RMB;
Mesh &gt; Edges &gt; Edge Slide ( or GG) to enable Edge Slide. E to toggle Even, if the current result is in a wrong way, then F to flip it (those are options shown on 3D View header).
Move to the expected position, then LMB or Enter to apply changes.


P.S.: For the 3rd step, you can simply CtrlB to bevel those edges. However, the normals for both islands are opposite in your case, you need to unify them before that.